When Mike and Sulley are first shown their room at the fraternity house, the light switch is under the top bunk bed. In subsequent shots it has moved closer to the door and is no longer directly under the bed.
In the opening scene, when Mrs. Graves is counting students, she counts to 19 and then notices that Mike is missing, which means that there are 20 students in the class. If this were the case, he wouldn't have to pair up with the teacher. However, one of the students could have two heads, similar to Terry and Terri - though they are considered two separate entities, Mike could not conceivably pair up with one of them while the other already has a partner.
In Monsters Inc., Mike tells Sulley "You've been jealous of my good looks since the fourth grade, pal." However, according to this movie, they did not meet or become friends until they went to college together. The producers have stated that Mike was merely using an expression.